The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X  1  X  1  1  X
 0  1  0  0  0  1  1  1  0  0  1  1 X+1  1  0  0  1
 0  0  1  0  1  1  0  1  0  1  1  0  0  X  0  1  1
 0  0  0  1  1  0  1  1  1  0  1  1  X X+1  0  1  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+75x^8+48x^9+364x^10+448x^11+966x^12+1728x^13+2772x^14+3648x^15+4183x^16+4640x^17+3704x^18+3648x^19+2772x^20+1728x^21+1256x^22+448x^23+189x^24+48x^25+92x^26+6x^28+4x^30

The gray image is a linear code over GF(2) with n=34, k=15 and d=8.
This code was found by Heurico 1.16 in 4.24 seconds.